1. Field of the Invention
This invention relates generally to communication transmitters, receivers, and systems. More particularly, the invention relates to a class of single sideband frequency modulation (SSB-FM) algorithms and their use in designing trellis based modems.
2. Description of the Related Art
Modulation techniques that can pass more information through a fixed bandwidth are generally desirable. Specific needs exist for improved bandwidth-efficient modulation schemes for use in applications like DSL modems, cable modems, broadband wireless access (e.g., WiMAX, 802.16, 802.16a), wireless local area networks (e.g., WiFi, 802.11), personal area networks (e.g., Bluetooth), terrestrial HDTV channels, digital cable TV channels, satellite communications, cellular telephones, wide-area cellular telephony based endpoints (e.g., GSM EDGE, 2.5 G, 3 G and 4 G terminals and base stations), and the like.
In the prior art, an example of a bandwidth-reducing modulation scheme is single sideband (SSB) modulation. SSB techniques use a Hilbert transform to halve the bandwidth that would have been needed to send the same information using double sideband AM. A suppressed-carrier double sideband amplitude modulated signal (DSB-AM) is formed by amplitude-modulating a real-valued message signal m(t),xDSB-AM(t)=m(t).  (1)A single sideband AM (SSB-AM) signal can be constructed by first constructing a SSB baseband signal according toxSSB-AM±(t)=m(t)±j{circumflex over (m)}(t)  (2)and then generating the SSB-AM signal at carrier frequency ωc as
                                                                                          s                                      SSB                    ±                                                  ⁡                                  (                  t                  )                                            =                                                A                  2                                ⁡                                  [                                                                                                              x                                                      SSB                            -                                                          AM                              ±                                                                                                      ⁡                                                  (                          t                          )                                                                    ⁢                                              ⅇ                                                  j                          ⁢                                                                                                          ⁢                                                      ω                            c                                                    ⁢                          t                                                                                      ±                                                                                            x                                                      SSB                            -                                                          AM                              ±                                                                                *                                                ⁡                                                  (                          t                          )                                                                    ⁢                                              ⅇ                                                                              -                            j                                                    ⁢                                                                                                          ⁢                                                      ω                            c                                                    ⁢                          t                                                                                                      ]                                                                                                        =                                                A                  ⁢                  Re                                ⁢                                  {                                                                                    x                                                  SSB                          =                                                      AM                            ±                                                                                              ⁡                                              (                        t                        )                                                              ⁢                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                                                  ω                          c                                                ⁢                        t                                                                              }                                                                                        (        3        )                                =                                            AM              ⁡                              (                t                )                                      ⁢                          cos              ⁡                              (                                                      ω                    c                                    ⁢                  t                                )                                              ∓                      A            ⁢                                          m                ^                            ⁡                              (                t                )                                      ⁢                          sin              ⁡                              (                                                      ω                    c                                    ⁢                  t                                )                                                                        (        4        )            where, A is a scalar, {circumflex over (m)}(t) is the Hilbert transform of m(t), and the subscripts + and − represent the upper lower sidebands respectively. The above SSB-AM signal can be viewed as a quadrature multiplexed signal where the message m(t) is transmitted on the in-phase (I) channel and the Hilbert transform of the message, {circumflex over (m)}(t), is transmitted on the quadrature (Q) channel to cancel out one sideband of m(t)'s DSB spectrum.
Prior art SSB bandwidth reduction is predicated on the fact that the baseband signal is real. Hence, SSB-AM techniques are not typically applied to signaling schemes in which the baseband signal is complex, such as in angle modulation. Angle modulation includes frequency modulation (FM) and phase modulation (PM). In angle modulated systems, the baseband signal is of the formxFM,PM(t)=eja(t)  (5)where a(t) is an information-carrying baseband phase function. When equation (5) is used to angle modulate a carrier, a constant-envelope double sideband (DSB) angle modulated passband signal results:sFM,PM(t)=ARe{xFM,PM(t)ejωct}=A cos [ωct+a(t)],  (6)where A is the signal amplitude. In FM, the instantaneous frequency of a(t) is varied according to an information signal, while in PM, a(t) is directly varied according to the information signal.
In the prior art, mathematical difficulties arise when one attempts to apply SSB-AM bandwidth reduction techniques to angle modulated signals. This is because SSB-AM methods assume a real message signal, which is processed according to equations (2) and (3) to generate the SSB-AM passband signal. On the other hand, angle modulated systems involve the complex baseband signal of equation (5). If the standard SSB-AM method of equation (2) is applied using m(t)=xFM,PM(t) of equation (5), information is destroyed and the demodulation and recovery of the FM or PM signal becomes complicated or impossible.
The same kinds of technical problems arise if one attempts to apply SSB-AM bandwidth reduction methodologies to digital modulation/demodulation (modem) schemes that use angle modulation such as phase-shift keying (PSK), continuous phase modulation (CPM), and quadrature amplitude modulation (QAM). The baseband signals for such digital communication methods are complex as opposed to being real-valued, thus complicating the application of SSB bandwidth reduction techniques to these classes of signals.
Some previous researchers have made attempts to apply SSB-AM bandwidth reduction techniques to restricted classes of angle modulated systems. Prior art methods typically apply SSB-AM methodology to the phase signal, a(t), to produce an SSB-AM phase signal [a(t)+jâ(t)], and to then apply angle modulation using this modified, reduced bandwidth phase signal. When such prior art approaches are applied, the resulting modulated signal becomes:sφ(t)=ARe{ej[a(t)+jâ(t)]ejωct}=Ae−â(t) cos [ωct+a(t)].  (7)
The prior art techniques, though, have some deficiencies. While the phase signal a(t) has its bandwidth reduced by one half, the actual modulated signal according to equation (7) is not really a SSB angle modulated signal, and generally has a bandwidth greater than exactly half the bandwidth of the corresponding DSB signal. In fact, in the Berosian reference, it was found that the signal in equation (7) reduces the bandwidth compared to the DSB signal by roughly one third as opposed to one half. Worse yet, due to the envelope term e−â(t) in equation (7), the modulated signal can have very high amplitude fluctuations. Still, because the phase angle a(t) in equation (7) remains the same as the standard FM or PM signal, demodulation reduces to equalizing the amplitude envelope and applying a standard FM or PM demodulator.
The Khan and Thomas reference discusses the bandwidth and the detection of the angle modulated signals of the form of equation (7). In the Chadwick reference, it is observed that for the special case of BPSK, x(t) in (5) reduces to a real quantity, and the signal in (7) is thus a true SSB-AM signal whose bandwidth is reduced by exactly one half. In the Nyirenda and Kom reference, the same method given by equation (7) is applied to full response continuous phase modulated (CPM) signals, to include minimum-shift keyed (MSK) signals. The results presented for MSK signals show that the bandwidth of the corresponding signal of equation (7) is about one third lower than that of ordinary MSK signals.
What is needed is a single sideband angle modulation technique that could reduce the bandwidth of a broad class of angle modulated signals by exactly one half. Also needed is a new class of quadrature multiplexed modems that use basic SSB bandwidth reduction concepts but have no need to compute Hilbert transforms in the transmitter and receiver structures.
It would be desirable to have SSB angle modulation techniques that could be applied to both continuous phase and discontinuous phase modulated signals. It would be desirable if such techniques could be applied to both constant-envelope signals and to non-constant envelope signals such as QAM and multi-amplitude CPM. It would be still more desirable to have optimum receiver structures that could achieve the same theoretical and measured probability of error performance as their DSB counterparts, but using half the bandwidth.
It would also be desirable to start with a bandwidth efficient modulation scheme like a CPM scheme and to apply an SSB technique to further reduce the already efficient bandwidth by half. It would be desirable to have new SSB based modulation techniques that could be used to design transmitters and receivers for SSB-processed CPM signals, including CPM signals such as CPM signals with full and partial responses, trellis coded CPM, multi-h CPM, multi-T CPM, and nonlinear CPM. It would be desirable if the SSB technique could reduce the spectral occupancy of already spectral efficient CPM signals by exactly half. It would be desirable to have SSB processing techniques that could be used to design digital communication systems that transmit and receive digital communication signals in a smaller bandwidth, such as one half the bandwidth required without using the SSB technique. It would be desirable to be able to apply such a technique to modulation schemes such as Gaussian minimum-shift keying (GMSK), quadrature phase shift keying (QPSK), offset QPSK (OQPSK), minimum shift keying (MSK), continuous phase frequency shift keying (CPFSK), quadrature amplitude modulation (QAM), orthogonal frequency division multiplexing (OFDM), vestigial side band (VSB), as well as other digital modem methods.
It would be desirable to have receiver structures that involve trellis decoders to decode the SSB-processed modem signals. It would be desirable to have trellis coded modulation schemes to improve minimum path distance in the trellis encoders. It would be desirable to integrate such receiver structures with turbo decoders, so that SSB-processed modem signals could be transmitted over noisy channels, and the extra 100% of bandwidth afforded by the SSB-processing could be used to carry turbo-encoded redundancy information. It would be desirable to be able to start with a modem, apply an SSB-processing technique to reduce the modem's bandwidth requirement by a factor of two, but to then send SSB-processed modem signals in both the upper and lower sidebands, to enable a communication mode whereby the double the information could be sent in the original DSB communication bandwidth. It would be desirable to have frequency division multiplexed communication systems that could efficiently multiplex two or more sidebands worth of SSB-processed information into a compact amount of bandwidth.
It would be still be more desirable to eliminate any need to compute a Hilbert transform or its inverse to achieve the same bandwidth halving as is available from SSB. That is, it would be useful to develop modem methods and apparatus that could double the supportable data rate over previous methods, while at the same time avoiding the use of the Hilbert transform.
It would be desirable to be able to map a complex baseband signal to a real-valued envelope signal that carried in its own trellis memory structure the same to information as the complex signal. It would be desirable if the mapping could preserve the bandwidth of the original complex baseband signal. It would be desirable to be able to then map two such real baseband signals into a pair of quadrature phase carriers to double the bit that could be transmitted in a unit of bandwidth. It would be still more desirable if the real-valued envelope signal could encode multi-bit symbols so that a super-highly bandwidth efficient modulation scheme could be constructed to improve the performance relative to QAM by 10 dB or more.
It would also be desirable to develop carrier recovery loops, symbol timing recovery loops, and equalization methods for practical receiver implementations to aid in the reception of such modulated signals. It would also be desirable to develop both optimal and sub-optimal, low cost receiver structures. Also needed are OFDM and other forms of multi-carrier based communication systems that would be able to take advantage of the extra bandwidth and performance available to each of the collection of channel built around the improved modulation techniques. It would further be desirable to develop communication systems that also incorporated spread spectrum techniques the mix the added capabilities of the new modulation methods with advantages of spread spectrum systems. It would further be desirable to use the inventive methods and combinations to develop communication systems, for example, to support applications like DSL modems, cable modems, broadband wireless access (e.g., WiMAX, 802.16, 802.16a), wireless local area networks (e.g., WiFi, 802.11), personal area networks (e.g., Bluetooth), terrestrial HDTV channels, digital cable TV channels, satellite communications, cellular telephones, wide-area cellular telephony based data endpoints (e.g., GSM EDGE, 2.5 G, 3 G and 4 G), and the like.